Do you agree with the growing sentiment among many Americans that “less government is the best government”? What is the proper role for government with respect to social welfare? If the government is not responsible for "social security,” then who or what (if anything) should be responsible for providing the most basic necessities (food, jobs, shelter, education, healthcare) in order to secure Americans on a social level?

Firstly, this is not a new sentiment. Old arguments, instead, have a way of becoming new again. The argument regarding "less government" has been around since the birth of the United States and was one of the planks in the Democratic-Republicans' platform from the 1770s to the early-1800s.
There is no objective answer to this question, but you can use objective information—both current events and history—to help you form your own response.
Though there are multiple political parties in the US, Democrats and Republicans dominate national, state, and local politics. Therefore, it would be most useful to look at what these parties think about the role of government in determining social welfare. Generally, current Democrats think that it is important to protect safety-net social programs, such as Social Security, Medicaid, and Medicare, because the absence of such programs will make lower-income, elderly, and handicapped citizens more vulnerable to dire poverty and homelessness. They insist that tax revenue must fund such programs.
Republicans, on the other hand, believe that there should be less dependency on such programs. There are some conservatives who want to make spending cuts, while there are others who would like to get rid of the programs altogether. They believe that healthcare and retirement are matters of personal investment and choice, and such matters are better left to the private sector. As for those in need, they believe that communities, particularly charities, could look out for those who cannot care for themselves. The belief among some Republicans is that local communities know best what their neighbors need—not the government. The belief among Democrats is that, while charity is certainly valued, it does not guarantee assistance to all who are in need. The federal government, they insist, must provide for the greater good. This includes providing EBT cards so that welfare recipients can shop for food and ensuring that every child has access to an education.